Search course

Use the search function to find more information about the study programmes and courses available at Chalmers. When there is a course homepage, a house symbol is shown that leads to this page.

Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TIF106 - Non-equilibrium processes in physics, chemistry and biology
Syllabus adopted 2014-02-25 by Head of Programme (or corresponding)
Owner: MPCAS
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Bioengineering, Chemical Engineering, Engineering Physics
Department: 16 - PHYSICS

Teaching language: English
Open for exchange students
Block schedule: D

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0111 Examination 7,5 c Grading: TH   7,5 c   29 May 2018 pm SB,  06 Oct 2017 am SB,  27 Aug 2018 am SB

In programs

MPNAT NANOTECHNOLOGY, MSC PROGR, Year 1 (compulsory elective)
MPAPP APPLIED PHYSICS, MSC PROGR, Year 1 (compulsory elective)


Professor  Bernhard Mehlig


MCC010   Statistical physics II MCC011   Non-equilibrium processes in physics, chemistry and biology TIF105   Stochastic processes in physics, chemistry and biology

  Go to Course Homepage


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Mathematical analysis and Algebra. Introductory level Thermodynamics and Statistical Physics, Classical and Quantum Mechanics


The great majority of physical, chemical, and biological processes occur
outside the thermodynamic equilibrium. How do we describe many-particle
system driven away from equilibrium, or evolving towards the equilibrium
due to an interaction with an environment? In contrast to the universality
of the thermodynamics, the non-equilibrium evolution is system specific
and requires individual approach. The purpose of the course is to
introduce basic concepts of kinetic theory and stochastic processes,
and to study practical tools to investigate non-equilibrium states. We will discuss the origin
of irreversible evolution and dissipation, hierarchy of relaxation processes, transport phenomena and noise, Brownian motion.
The course includes a selection of applications to quantum solid state systems,
chemical reaction kinetics, and soft matter like colloidal dispersions, polymers, gels,
glasses and biological systems.

Learning outcomes (after completion of the course the student should be able to)

After this course, the student should have acquired a general knowledge of stochastic processes and their use to describe the time evolution of systems in nature. More specifically, the student should be able to:
* describe basic concepts of the kinetic theory for classical and quantum many particle systems
* describe the origin of irreversible evolution of physical, chemical, and biological systems, and the hierarchy of relaxation processes
* practically solve transport problems, as well as analyze dissipative and fluctuation phenomena, and the effects of an environment.


The following topics are covered:
Statistical description of a dissipative macroscopic system and origin of irreversible evolution. Stochastic processes and basic distributions.
Boltzmann equation and transport theory.
Langevin theory of classical and quantum Brownian motion.
Fluctuation and noise.
Applications to physical, chemical and biological systems.

The first half of the course deals with general concepts of non-equilibrium statistical physics and methods to describe dissipative and transport processes in many-body systems. Starting with a simple example of a random walk the basic concepts in probability theory and stochastic processes are introduced. More complex systems are studied via the Boltzmann equation and by considering Markov processes. The latter introduces the study of Master-, Fokker-Planck- and Langevin equations.

The student can choose two different directions for the second part of the course:

1. Quantum non-equilibrium systems
Here we consider applications in modern solid state physics, quantum electronics and optics. We study methods to describe the state and evolution of quantum non-equilibrium systems, linear response theory, problem of quantum noise, relation between fluctuations and dissipation, behavior of quantum particle in an environment.

2. Transport in soft matter and biological systems
Here we study applications in complex systems. We study methods to describe transport processes in various systems like polymers, colloids, soft matter. Description of chemical reactions and Brownian motors. Applications to systems in phsyics, chemistry and biology.


The course is based on a series of lectures and exercises. The second half of the course can be organized as a project work.


The content of the course will be covered in lecture notes. Additional reading material (course book) will be specified on the course homepage.


Written examination and home assignments.

Page manager Published: Thu 04 Feb 2021.